A characterization of the groups and by their -fusion systems, q odd

Abstract

Abstract Let q be a nontrivial odd prime power, and let $n \ge 2$ be a natural number with $(n,q) \ne (2,3)$ . We characterize the groups $PSL_n(q)$ and $PSU_n(q)$ by their $2$ -fusion systems. This contributes to a programme of Aschbacher aiming at a simplified proof of the classification of finite simple groups.